As hurricane season begins this week, experts are still trying to count the number of deaths caused by last year’s devastating Hurricane Maria in Puerto Rico. The latest estimate: roughly 4,600, many of them from delayed medical care.

Residents of Puerto Rico died at a significantly higher rate during the three months after the hurricane than they did in the previous year, according to the results of a new study by a group of independent researchers from Harvard T.H. Chan School of Public Health and other institutions.

The researchers say their estimate, published Tuesday in The New England Journal of Medicine, remains imprecise, with more definitive studies still to come. But the findings, which used methods that have not been previously applied to this disaster, are important amid widespread concerns that the government’s tally of the dead, 64, was a dramatic undercount.

Winds, flooding and landslides swept away homes and knocked out power, water and cellular service, which remained largely unrepaired for months.

Researchers for this latest study visited more than 3,000 residences across the island and interviewed their occupants, who reported that 38 people living in their households had died between Sept. 20, when Hurricane Maria struck, and the end of 2017. That toll, converted into a mortality rate, was extrapolated to the larger population and compared with official statistics from the same period in 2016.

Because the number of households surveyed was relatively small in comparison to the population’s size, the true number of deaths beyond what was expected could range from about 800 to more than 8,000 people, the researchers’ calculations show. The toll exceeded previous estimates, researchers said, in part because they looked at a longer time period.

About 15 percent of the people interviewed reported that someone in their household was unable to get medicines for at least a day after the storm. Roughly 10 percent said that a household member had trouble using breathing equipment, which often relies on electricity. Fewer than 10 percent reported closed medical facilities and 6 percent said doctors were unavailable. The study estimates that about a third of the deaths were caused by a delay in medical care or the inability to obtain it.

Under pressure, the government announced in December that all deaths that occurred after Maria hit would be reviewed and that people who died either directly or indirectly from the storm and its aftermath would be included in a revised tally. The government commissioned a review by researchers at the Milken Institute School of Public Health at the George Washington University, who had promised an initial report in May. But that analysis has barely begun. “They’re still acquiring data,” said Dr. Lynn R. Goldman, the school’s dean. The study will use the territory’s vital records and information from funeral homes, the medical system and the larger public.

Dr. Goldman now says she expects to deliver the initial review, which will cost $305,000, sometime this summer, with a more definitive analysis involving interviews with survivors and requiring additional funding following perhaps nine months later. She said she and her colleagues were delayed because they had failed to anticipate the need for the university to navigate different tax laws in preparing their contract with the government of Puerto Rico.

The newly released study, by contrast, was conducted for about $50,000 without the participation of the territory’s government, which the researchers said refused to provide data to them.

On Tuesday, the government of Puerto Rico said it welcomed the new survey and looked forward to analyzing it. Carlos S. Mercader, executive director of the Puerto Rico Federal Affairs Administration, said that both the Harvard survey and the George Washington University study will help Puerto Rico “better prepare for future natural disasters and prevent lives from being lost.”

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A collapsed building on top of a car in Puerta de Tierra, San Juan, P.R., following Hurricane Maria.CreditErika P. Rodriguez for The New York Times

Results were produced quickly and at a modest cost by focusing on a randomized sample of the population, and by using mobile mapping technology and an army of graduate students to conduct the survey.

“It helped that a lot of them were psychology students, because they were going to be dealing with families in distress,” said Dr. Satchit Balsari, a research fellow at Harvard FXB Center for Health and Human Rights and one of the study’s senior authors.

The researchers found that many people had been displaced from their homes and had endured months without essential utilities, especially in remote areas. Those challenges affected the researchers, too, who downloaded digital map data before traveling to areas that still lacked cell service in early 2018.

The surveyors used off-road vehicles because of the continuing threat of landslides in mountain areas. In part of Culebra, a small island off the main island of Puerto Rico, they arrived planning to interview 35 households. Only one person remained. “It was a bathroom and half a room,” said Domingo J. Marqués, an associate professor of psychology at Albizu University San Juan, who helped conduct the study with his students and who himself lacked power and running water for months after the hurricane. “All the other houses were gone.”

Those conditions, he said, made clearer why the government’s official death count was incomplete. “Even if they were really doing a good job, it was really hard unless you did something like we did — go talk to people on the ground,” he said. People, he added, “died alone in their houses. Nobody went there. Some of them were covered by a landslide, and months after they’ve not recovered the bodies.”

Notably, abnormally high death rates continued at least through the end of December. “They didn’t show any sign of coming down in the several months following the hurricane that we were looking at,” said Caroline Buckee, an associate professor of epidemiology at the Harvard School of Public Health and the study’s other senior author.

“There is clearly an excess mortality, and let’s not argue very specific numbers,” said Dr. Gilbert Burnham, a professor of international health and founder of the Center for Humanitarian Health at Johns Hopkins University, who was not involved in the research, but has performed similar studies assessing deaths, including in Mosul, Iraq.

Dr. Burnham said that despite the study’s limitations, including the difficulty of estimating Puerto Rico’s total population in light of migration, and the possible oversampling of smaller populations in more remote areas, such surveys “should become a standard activity in post-disaster situations,” because they help reveal vulnerabilities that can be addressed to save lives.

Dr. Burnham and another expert unaffiliated with the study agreed with the researchers that the toll could be even higher than estimated if adjusted for the fact that people who died alone could not be surveyed. “It just is stunning how poor our information was as to what was happening in Puerto Rico,” said Leslie Roberts, a professor and director of the program on forced migration and health at the Columbia University Mailman School of Public Health.

The use of surveys to assess the extent of deaths and suffering in disasters, and to guide improvements, extends back decades. Particularly important was a series of studies in Bangladesh in 1970 and 1971, which revealed that women died at a higher rate than men from a massive cyclone that the researchers estimated killed at least 224,000 people.

In Puerto Rico, the researchers visited 104 barrios across the island, selecting them to ensure that both urban and nonurban areas were represented. In the areas most remote from cities, about one in five residences were abandoned. The researchers chose households at random in each of the barrios, asking about deaths in the home, deaths in the neighborhood, and access to electricity, running water and phone service.

“The situation is not over,” Dr. Marqués said. “We still have people without power, without running water, and it’s already hurricane season again.”

He added, “We hope our data helps the government develop some more specific continuity plans so they can prepare for proper general health and also mental health planning.”

A version of this article appears in print on , on Page A13 of the New York edition with the headline: Hurricane’s Death Toll In Puerto Rico May Top 4,600, New Study Says. Order Reprints | Today’s Paper | Subscribe